Bornological spaces of non-Archimedean valued functions with the point-open topology
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- by W. Govaerts
- Proc. Amer. Math. Soc. 72 (1978), 571-575
- DOI: https://doi.org/10.1090/S0002-9939-1978-0509257-8
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Abstract:
F denotes a nontrivially non-Archimedean valued field with rank one, X an ultraregular space and $C(X,F,p)$ is the vector space $C(X,F)$ of all continuous functions from X into F with the topology p of pointwise convergence. We show that $C(X,F,p)$ is a bornological space if and only if X is a Z-replete space. Also, some results are found concerning the compact-open topology c and we make a comparison with that case as studied by Bachman, Beckenstein, Narici and Warner.References
- George Bachman, Edward Beckenstein, Lawrence Narici, and Seth Warner, Rings of continuous functions with values in a topological field, Trans. Amer. Math. Soc. 204 (1975), 91–112. MR 402687, DOI 10.1090/S0002-9947-1975-0402687-6
- S. Mrówka, Further results on $E$-compact spaces. I, Acta Math. 120 (1968), 161–185. MR 226576, DOI 10.1007/BF02394609
Bibliographic Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 571-575
- MSC: Primary 46P05; Secondary 46E15, 54C40
- DOI: https://doi.org/10.1090/S0002-9939-1978-0509257-8
- MathSciNet review: 509257